Synchrotron-radiation-based determination of Xe L-subshell Coster-Kronig yields:
A reexamination via high-resolution x-ray spectroscopy
W. Cao,1,*J.-Cl. Dousse,1J. Hoszowska,1M. ˇZitnik,2M. Kavˇciˇc,2and K. Buˇcar2
1Department of Physics, University of Fribourg, Ch-1700 Fribourg, Switzerland
2J. Stefan Institute, SI-1001 Ljubljana, Slovenia
The xenonL-subshell Coster-Kronig (CK) transition yields were revisited via high-resolution measurements of theLα1,2(L3−M4,5) andLβ1(L2−M4) x-ray emission lines. TheLx-ray spectra were measured employing a Johansson-type curved crystal spectrometer and energy-tunable synchrotron radiation. The CK yields were derived from the relative Lx-ray intensity jumps at theL edges by fitting the fluorescence intensities as a function of the photon energy to theL-subshell photoionization cross sections. The latter were obtained from the measuredL-edge photoabsorption spectrum. Values of 0.118±0.029, 0.383±0.037, and 0.096±0.016 were found for thef23,f13, andf12CK yields, respectively. Thanks to high resolution, theL1fluorescence yield of 0.059±0.002 was also determined from intensity ratios of the well-resolvedLβ4(L1−M2) andLβ1(L2−M4) lines.
PACS number(s): 32.70.−n, 32.80.Hd, 32.50.+d, 32.30.Rj
I. INTRODUCTION
The decay scheme of atomic inner-shell vacancies is branched into cascades of radiative and nonradiative Auger transitions. The Coster-Kronig (CK) transitions are the fastest Auger transitions, in which the vacancy transfers within the same major shell. The vacancy transfer probability from the isubshell to the higherj subshell is called the CK yieldfij. CK rates depend on the initial- and final-state wave functions and are very sensitive to electron binding energies as well as to solid-state effects [1,2].
Particularly interesting is the region aroundZ=48 where a sharp decrease in the f13 value is expected due to the L1−L3M4,5 transitions becoming energetically forbidden.
Large discrepancies between the theoretical [2,3] and existing experimental results [4,5] point out the need for new accurate data. Experimental determination of the L-shell CK yields presents, however, considerable difficulties. For this reason, data are scarce and often suffer from large uncertainties [6].
To date, to determine thef23 yields, mostly theKα-Lx-ray coincidence method [6,7] was used. This technique, however, fails in the case of the L1-subshell CK yields due to the dipole forbiddenK−L1radiative transition. The alternative photoionization experimental method was limited to the use of radionuclides [8].
The subshell-selective photoionization method based on energy-tunable monochromatic synchrotron radiation [9]
offers the possiblity to measure all L-subshell CK yields.
This method has been successfully applied to determine CK yields for solids [9–13] as well as for Xe [14]. So far, most measurements of the x-ray fluorescence lines were performed by means of energy-dispersive semiconductor detectors. In our recent work on Pd (Z =46) [15], the subshell-selective photoionization method was combined with high-resolution x-ray spectroscopy, allowing even the partialL1−L3M4,5CK yield to be deduced. By applying this technique to elements
*wei.cao@unifr.ch
within the mid-Z region, it would certainly be possible to reveal theL1CK yield cutoff trend.
In this article, we report on the revisit of theL-subshellf23, f13, andf12CK yields for xenon (Z=54) via the synchrotron- radiation-based high-resolution x-ray spectroscopy technique.
The individualL-subshell photoionization cross sections were determined from the measured x-ray-absorption spectrum.
The measurements of theLα1,2 (L3−M4,5) andLβ1 (L2− M4) lines were carried out by means of a high-resolution, Johansson-type crystal x-ray spectrometer. The CK yields were derived from the variation of the Lα1,2 and Lβ1
fluorescence-line intensities at the absorptionLedges due to the onsets of CK vacancy transfers. In addition, theL1-subshell fluorescence yieldω1was also determined from intensity ratios of the well-resolvedLβ4andLβ1lines.
II. EXPERIMENT
The measurements were performed at the x-ray absorption fine structure (XAFS) beamline of Elettra synchrotron in Trieste, Italy, employing the x-ray spectrometer of the Joˇzef Stefan Institute [16]. The primary x-ray beam was monochro- matized by means of a double-crystal Si(111) monochromator, and higher harmonics were reduced with a Pt-coated mirror.
The photon flux incident on the Xe sample was ∼1010 photons/s. The Xe gas was contained in a 10-mm-long stainless-steel cell sealed with 12.5-μm-thick Kapton foils.
Two ionization chambers, one in front and one after the spectrometer, were used for the absorption measurements and also for normalization purposes. The experimental setup was similar to the one described in [17].
For the absorption measurement, the Xe gas pressure was kept at a nominal value of 500 mbar. In order to obtain both a high enough photon beam transmission and detector efficiency, the percentages and pressures of the helium-nitrogen gas mixtures for each of the ionization chambers were optimized.
The photon energy was tuned with 0.2-eV steps in the range from 4500 to 5800 eV. Another scan over the same energy range was performed with an empty target cell in
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Published in "Physical Review A 81(1): 012501, 2010"
which should be cited to refer to this work.
order to determine the residual attenuation in the Kapton windows and in the ionization chambers. For the fluorescence measurements, the Xe gas pressure was 200 mbar.
The L x-ray fluorescence lines of Xe were measured at an angle of 90◦ with respect to the horizontally polarized incident photon beam. A cylindrically curved quartz (10¯10) crystal in the second order of reflection was employed. The diffracted x rays were recorded with a thermoelectrically cooled (−40◦C), back-illuminated CCD camera consisting of 770×1153 pixels with a pixel size of 22.5×22.5μm2. The x-ray spectrometer energy resolution was about 0.2 eV. For normalization purposes, the incident photon flux was recorded online with the first ionization chamber each 10 s. Beam intensities were corrected for absorption in the ionization chamber and the Kapton windows in the beam path.
The fluorescence spectra were calibrated using the ref- erence energies of the Lα1 (or Lβ1) x-ray line reported in Ref. [18]. Depending on the incident photon energy and the total photon number, the time to collect anLx-ray spectrum varied from 50 to 170 min. A series of 14 Lα and another series of 7 Lβ1 x-ray emission spectra were recorded. The incident-beam energy was tuned from 4850 eV (68 eV above theL3-edgeE3) to 5700 eV (247 eV above theL1-edgeE1) for the measurements of theLαlines and from 5200 eV (96 eV above theL2-edgeE2) to 5750 eV (297 eV aboveE1) for theLβ1andLβ4lines.
III. DATA ANALYSIS A. Spectra fitting
The XeLαandLβ1x-ray spectra measured at two different photon energies are shown in Figs.1and2, respectively. It can be seen that the high-resolution x-ray emission spectroscopy employed in our work permits us to resolve the individual
0.0 0.2 0.4 0.6 0.8 1.0
4080 4100 4120 4140
0.0 0.2 0.4 0.6 0.8 1.0
(b) E=5600 eV
Normalized Intensity
E=4950 eV (a)
Energy (eV)
FIG. 1. (Color online) Fitted high-resolutionLαx-ray spectra of Xe at different incident-beam energies: (a)E=4950 eV and (b)E= 5600 eV. Solid thick lines represent the total fit to the experimental data (dots) and dashed lines the individual components.
0.0 0.2 0.4 0.6 0.8 1.0
4360 4380 4400 4420 4440 4460 4480
0.0 0.2 0.4 0.6 0.8 1.0
E=5700 eV
Normalized Intensity
E=5250 eV (a)
Energy (eV) (b)
FIG. 2. (Color online) Fitted high-resolution Lβ1 (L2−M4) x-ray spectra of Xe at different incident-beam energies: (a) E= 5250 eV and (b)E=5700 eV. Solid thick lines represent the total fit to the experimental data (open circles) and dashed lines the individual components. In (b), the peak on the high-energy side of theLβ1line corresponds to theLβ4(L1−M2) transition.
Lα (or Lβ) x-ray transitions, thus avoiding an elaborate fitting procedure such as is needed in the case of L-x-ray spectra measured with energy-dispersive detectors [13]. In inner-shell photoionization, however, the diagram transitions may be accompanied by satellite lines resulting from additional vacancies present in outer subshells via Coster-Kronig and shake [19] processes. Due to the reduced screening of the nuclear charge, the x-ray satellite lines are shifted in energy with respect to the diagram transitions.
Multiconfiguration Dirac-Fock calculations [20] show that the first-order N and O satellites are not resolved from the Lα and Lβ1 parent lines. This overlap of the LN and LO satellite transitions with the parent diagram lines results in a nonlifetime broadening of the latter. Our calculations, performed within the framework of the sudden approximation model using self-consistent Dirac-Fock wave functions from the code of reference [20], predict for theO-shake probability a value of 0.14 and for theN-shake 0.05. Although theO-shell electron-shake contribution is non-negligible, the fluorescence intensity jumps are not affected because it is constant over the measured photon energy range. The same holds for the N-shell shake contribution. For incident-beam energies tuned above theL1edge, the opening of theL1−L3N CK channel results in an asymmetry on the high-energy flank of theLα1
line [see Fig. 1(b)]. The LαM satellite transitions, expected at ∼13 eV above the Lα1 line, were not observed. This is not surprising because theL1−L3M CK transitions are energetically forbidden and theM-shake probability of 0.006 is negligibly small.
By taking these considerations into account, eachLα1,2line was fitted by two Lorentzians with widths as free parameters.
Above the L1 edge, an additional Lorentzian profile was needed to account for the Lα1N satellite contribution. For
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theLβ1line as well as for theLβ4 (L1−M2) line observed for photon impact energies tuned above the L1 edge [see Fig.2(b)], a single Lorentzian profile was used because the L1−L2N CK transitions are very weak. The fitted Lx-ray intensities were normalized to the same incident photon flux and data acquisition time. In addition, each spectrum collected at an incident energyEwas weighted by the corresponding beam-absorption correction factor
Fcorr(E)= μ(E)b
1−exp[−μ(E)b], (1)
which is valid for a perpendicular experimental geometry [21].
The total attenuationμ(E)b, wherebstands for the interaction path, was measured at a target gas pressure of 200 mbar in the beam energy range 4500 eVE5800 eV with 1-eV steps.
B. L-subshell cross-section parametrization
The experimentalLα fluorescence intensityI(E) is pro- portional to the totalLx-ray production cross section
σLαX(E)=ωLα[σ3(E)+f23σ2(E)
+(f13+f12f23+f13 )σ1(E)], (2) whereσi(E) are theLi(i=1, 2, or 3) subshell photoionization cross sections andf13 denotes theL1toL3hole transfer rate resulting from theL1−L3radiative transition. TheωLαstands for theLαdiagram-line fluorescence yield. Similarly, theLβ1
and theLβ4x-ray production cross sections are σLβX1(E)= Lβ1
2
[σ2(E)+f12σ1(E)] (3) and
σLβX4(E)= Lβ4
1
σ1(E)= Lβ4
1radω1σ1(E), (4) respectively.Lβ1 andLβ4represent the fluorescence widths of the two transitions,1and2the total widths of theL1and L2subshells, and1radthe radiative width of theL1subshell.
In order to derive the CK yields from the measuredLx-ray fluorescence intensities, the variation of the photoionization cross sections with photon energy should be known. It is generally assumed that within a certain energy range, the cross sections vary smoothly with photon energy and the dependence can be described by a power law. According to the independent particle approximation (IPA) calculations, the singleLi-subshell photoionization cross sectionσifor Xe can be expressed as
σi(E)=aiEbi, (5) whereaiis in the unit of Mbarn andEin keV.
The XeL-shell photoionization cross sections are shown in Fig.3. Because the temperature and pressure of Xe in the gas cell could not be determined accurately, the measured Xe L-edge absorption spectrum was normalized to the L3-pre- edge x-ray absorption coefficients reported by Wuilleumier [22]. TheL3-pre-edge attenuation coefficients were fitted with the power law and extrapolated in order to get the totalL-shell photoionization cross section.
Below theL2edge, theL3-subshell ionization cross section is given by the measured totalL-shell photoionization cross
4.8 5.0 5.2 5.4 5.6 5.8
0.00 0.04 0.08
0.12 Experiment
Extrapolated curve
Jitschin 1995
Ionization cross section (Mbarn)
Incident Beam Energy (keV) L1-edge L2-edge
L3-edge
FIG. 3. (Color online) Experimental and theoreticalL-subshell photoionization cross sections of Xe. The solid lines are the extrapolated curves obtained by scaling the analytical expression given by Eq. (5) to the measured values (open circles). The dashed lines are the theoretical values given by Jitschinet al.[14].
section. The latter is depicted by circles in Fig.3and compared to the power-law dependence of Jitschinet al.[14] shown by the dashed line. Obvious deviations of our experimental values from those based on the IPA calculations are observed. These differences could be due to many-body and multi-ionization effects. However, in the region slightly below theL2edge, the slopes of our experimental and IPA theoretical curves match each other quite well. Thus, adopting for the parameterb3the value of Jitschinet al. [14], the curve given by Eq. (5) was just scaled down to match the experimental points before the L2 edge. Above the L2 edge, the rescaled power-law curve was used to extrapolate the L3-subshell cross section which was then subtracted from the experimental values to get the L2andL2- plusL1-subshell cross sections for incident-beam energiesE2< E < E1 andE > E1, respectively. Similarly, theL1-subshell cross section was obtained by subtracting the extrapolated values from the rescaled power-law curve for the L2-subshell cross section. The parametersai of the rescaled extrapolation curves together with the parametersai andbiof Jitschinet al.[14] are listed in TableI. The fitted curves are depicted with solid lines in Fig.3.
IV. RESULTS AND DISCUSSION
The method used to get the CK yields for Xe is similar to the one reported in our previous work [15]. Thef23CK yield was extracted from theLαintensity jump at theL2edge. First, the fluorescence intensity below the L2 edge was fitted with TABLE I. The fitting parameters for the power-law dependence of theLi-subshell (i=3,2,1) photoionization cross sections.
Parameter i
3 2 1
ai(Mbarn) 7.640 4.076 –
ai[14] (Mbarn) 7.818 3.716 0.467
bi[14] −2.753 −2.654 −1.765
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the following expression:
I3(E)=CωLασ3(E), (6) whereCis the instrumental proportionality constant. From the fit, the parameterA3=CωLαwas obtained. To derive the CK contribution, the fluorescence intensities I3(E) for energies above theL2edge were extrapolated and subtracted from the I(E) data. For incident-beam energies between theL2andL1
edges, the values
I2(E)=I(E)−I3(E) (7) correspond to the additional fluorescence intensities due to theL2−L3CK process. From the fit ofI2(E), the parameter A2=f23CωLα was obtained. Finally, the f23 CK rate was derived from the ratio ofA2toA3:
f23= A2
A3
. (8)
Similarly, thef13CK yield can be expressed as f13= A1
A3
−f12f23, (9) where thef12 yield is given by theLβ1 intensity jump at the L1edge:
f12= A1
A2. (10)
Here, A is introduced to distinguish the Lα and Lβ1
intensities. The fitting parameters for theLβ1line intensities areA2 =CωLβ1andA1=f12CωLβ1, where the instrumental proportionality constant isCdue to the changes of the crystal and detector positions. The term f13 is omitted in Eq. (9) because the competing intrashell radiative transitionL1−L3
is negligibly weak compared to the CK process [12].
Results of the fitting procedure for the Lαintensities are presented in Fig.4. Values of 0.118±0.029, 0.383±0.037, and 0.096±0.016 were found for the f23,f13, andf12 CK yields, respectively. They are listed in the first row of TableII.
For comparison, CK yields adopted in the former work [14]
are listed in the second row. The theoretical predictions given
5.0 5.2 5.4 5.6
14 16 18 20 22
f13+f12f23
Lα12 Intensity (Arb. Units)
Incident Beam Energy (keV) f23
L2-edge L1-edge
FIG. 4. (Color online) TheLα1,2 x-ray fluorescence intensities (open squares) fitted with the measured photoionization cross sections (open circles). The solid lines show the corresponding extrapolated power-law curves.
TABLE II. Coster-Kronig rates and the L1 fluorescence yield for Xe.
f23 f13 f12 ω1
Present 0.118(29) 0.383(37) 0.096(16) 0.059(2)
Jitschin [14] 0.14(2) 0.23(4) 0.12(3) –
Chen [2] 0.174 0.328 0.196 0.048
Campbell [6] 0.159(40) 0.25(8) – –
Krause [23] 0.154(31) 0.28(4) 0.19(4) 0.046(9) Jitschin [14]a 0.115 0.185 0.095 – Jitschin [14]b 0.174 0.316 0.169 –
aResults with electron correlation corrections.
bResults without electron correlation corrections.
by Chenet al.[2], the values recommended by Campbell [6], and the semiempirical values reported by Krause [23] are also quoted. Our data for thef12andf23are in general smaller than the values from theoretical and semiempirical predictions but are consistent with the values adopted by Jitschinet al.[14].
For thef13CK rate, however, the listed values in TableIIdiffer:
Our value is closer to the one reported by Chenet al.[2], while the result from the work of Ref. [14] is closer to the one by Campbell [6]. To make a detailed comparison with the former work of Jitschin et al.[14], data with and without electron correlation corrections [14] are also presented in the table.
The current value forf13 is found to be closer to the result obtained in [14] from the IPA fit but much larger than the one with correlation corrections.
In order to get a more general view of theZ dependence for thef13 yield in this Z region, thef13 CK probabilities for Xe and the existing experimental results for neighboring elements Mo (Z=42) [12], Pd (Z=46) [15], and Ag (Z= 47) [12,24], and the recent results for Ba (Z=56) [25] and La (Z=57) [26] are compiled in Fig.5. It can be seen that
32 36 40 44 48 52 56 60
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Chen [2]
Sorensen [12]
Cao [15]
Cao [15] f LLN
13
Sorensen [11]
Jitschin [24]
Barrea [25]
Barrea [26]
Jitschin [14]
Jitschin [14]*
Jitschin [14]+ Present L 1-L 3 Coster-Kronig Yield
Atomic Number Z
FIG. 5. (Color online) Presentf13CK rate of Xe (open circle).
The datum is compared to theoretical values from [2], the available experimental data for the neighboring elements, Mo [12], Pd [15], Ag [11,24], Ba [25], and La [26], and for Xe [14] to the adopted value, as well as to values with (∗) and without (+) electron correlation corrections. The f13LLN denotes the Pd partial L1−L3N CK yield obtained in [15].
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our result is in reasonable agreement with values for higher Zelements (Ba and La) and with the partialL1−L3N yield for Pd.
Differences among thef13CK yield values can be attributed mainly to the determination of theLi-subshell photoionization cross sections. Limitations of the IPA model can be clearly seen in Fig. 3. The discrepancies between the IPA model and the fit to our experimental data could be due to mul- tiple ionization processes [27,28], electron correlation effects [29,30], quantum interferences between one- and two-electron excitation processes [31], or the dynamic screening effects [32]. Calculations including these effects could lead to a more precise totalL-shell photoionization cross section. This is an issue still under debate [33], which is, however, beyond the scope of our work.
When the energy of the photon beam is tuned above the L1 edge, both Lβ1 and Lβ4 transitions are observed in the measured spectrum [see Fig. 2(b)]. The intensity ratio of these two close-lying lines can be accurately cal- culated, giving the possibility to determine the ω1 fluo- rescence yield. This method is straightforward and free from elaborate spectrometer efficiency corrections [7,34].
Using Eqs. (3) and (4), theL1-subshell fluorescence yield is given by
ω1= ILβ4
ILβ1
Lβ1
Lβ4
rad1 2
[f12σ1(E)+σ2(E)]
σ1(E) . (11) By adopting for Lβ1 and Lβ4 the interpolated values of Campbell and Wang [35], and for the1radand2the calcula- tions of Chenet al.[2],ω1was found to be 0.059±0.002. This result is higher than the theoretical predictions of Chenet al.[2]
and Krause [23] and smaller than the value of 0.068±0.007 determined for Ba (Z=56) [25].
V. CONCLUSION
We have determined the Coster-Kronig transition yields for Xe via synchrotron-radiation-based high-resolution measure- ments of theL x-ray emission lines. By making use of the measured L-subshell photoionization cross sections and the power-law dependence of the photoionization cross sections on the primary photon energy, thef23andf13CK yields were derived from the relativeLα intensity jumps at theL edges and thef12 rate from theLβ1intensity jump at theL1 edge.
From the intensity ratios of the Lβ4 and theLβ1 lines, the fluorescence yield of theL1subshell was also determined.
Our results for thef12andf23CK yields were found to be consistent with those of Jitschinet al.[14], whereas for thef13
rate, a higher value was obtained. The discrepancy was mainly attributed to the different parameterization of theLiphotoion- ization cross sections and, in particular, to the limitations of the IPA model used by Jitschinet al.. Indeed, the multiple-electron excitation and many-body and time-dependent effects, which are implicitly included in our measured photoionization cross sections, were neglected in the IPA theoretical predictions. To further reduce the uncertainty of the CK values, more elaborate calculations would be needed. Experimentally, coincidence measurements between the CK electron and the photon or Auger electron emitted in the subsequent decay would allow the separation of theL3andL2photoionization cross sections above theL2andL1thresholds, respectively.
ACKNOWLEDGMENTS
We wish to acknowledge L. Olivi for the beamline operation during the experiments. This project was financially supported by the Swiss National Science Foundation (Grant No. 200020- 125124) and the program of the Slovenian Research Agency (Program No. P1-0112).
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